Geodesic
The average length of reduced regular continued fractions
Sbornik. Mathematics, Tome 200 (2009) no. 8, pp. 1181-1214

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $l(a/b)$ be the number of steps of the by-excess Euclidean algorithm applied to the numbers $a$ and $b$. In this paper we obtain a three-term asymptotic formula for the expectation of the random value $l(a/b)$, when $1\le a\le b\le R$ and $R\to\infty$. Bibliography: 11 titles.
Keywords: Euclidean algorithm, division by-excess, average length, continued fraction. 
@article{SM_2009_200_8_a4,
     author = {E. N. Zhabitskaya},
     title = {The average length of reduced regular continued fractions},
     journal = {Sbornik. Mathematics},
     pages = {1181--1214},
     publisher = {mathdoc},
     volume = {200},
     number = {8},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2009_200_8_a4/}
}
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E. N. Zhabitskaya. The average length of reduced regular continued fractions. Sbornik. Mathematics, Tome 200 (2009) no. 8, pp. 1181-1214. http://geodesic.mathdoc.fr/item/SM_2009_200_8_a4/